Einstein, Dirac, and Feynman

Both Dirac and Feynman were intensely interested in combining
quantum mechanics with special relativity. Paul A. M. Dirac
is known to us for his Dirac equation. Richard P. Feynman is
known to us for Feynman diagrams. In fact, these two great
physicists were interested in deeper foundational problems.

However, their approaches to physics were quite different.
Dirac was interested in mathematical formulas with esthetic
appeal. On the other hand, Feynman was interested in
observing what is happening in the world and fill in
mathematical formulas as needed.

Feynman's parton picture is one of his brilliant observations.
Yet, this is valid in the infinite-momentum system and
lacks Lorentz covariance. Thus, it is fun to look into
the possibility of making it covariant by filling in
mathematical formulas from Dirac's papers.

Photo by Bulent Atalay.

One way to do is to observe that both Dirac and Feynman were
quite fond of harmonic oscillators because they satisfy Dirac's
need for mathematical beauty, and also Feynman's need to fill
in mathematical formulas readily available.

Dirac never liked the present form of quantum mechanics based
on probabilistic interpretation. On the other hand, he held
the view that,if we accept this interpretation, this form of
quantum mechanics should be consistent with Lorentz covariance.
Dirac published the following papers on this subject.

In his effort to combine quantum mechanics with relativity, Feynman
first considered waves propagating in the Lorentz-covariant world,
resulting in Feynman diagrams. How about standing waves? Feynman
considered harmonic oscillators. Feynman would have liked to
give a covariant description his parton picture, but left this
problem as a homework problem for younger physicists. He wrote the
following provocative papers on this subject.

In 2004, Kim and Noz produced a documentation on this issue and
presented at an interdisciplinary science conference held in Natchitokes
(Louisiana, October 2004). The paper is written for non-experts, and
can be retrieved from the
ArXiv.

The photo of Dirac and Feynman is from the Caltech Photo Archive.
This photo was taken by Marek Holzman during the International
Conference on Relativity Theory of Gravitation in Warsaw (Poland)
on July 25-31 1962, organized by Leopold Infeld.